Residuated mapping - Revision history

en>Jochen Burghardt: /* top */ def.d residuated, to complete the motivation; removed "iff" from def.

2014-06-28T11:50:33Z

top: def.d residuated, to complete the motivation; removed "iff" from def.

← Older revision		Revision as of 13:50, 28 June 2014
Line 1:		Line 1:
	~~[[Image:Impossiball solved.jpg\|thumb\|The Impossiball in its solved state.]]~~
	~~[[Image:Impossiball scrambled.jpg\|thumb\|The Impossiball in a scrambled state.]]~~
	~~[[Image:Impossiball turned.jpg\|thumb\|The Impossiball partway through a turn, showing how the pieces lift up.]]~~

	The '''Impossiball''' is a rounded [[icosahedron\|icosahedral]] puzzle similar to the [[Rubik's Cube]]. It has a total of 20 movable pieces to rearrange, same as the Rubik's Cube, but all of the Impossiball's pieces are corners, like the [[Pocket Cube]].

	~~== History ==~~		Bonus: WP Twin and WP Twin Auto Backup: (link to ) While not a theme, I think this software is essential if you are maintaining your Wordpress blog or regularly create new blog sites. It is used by around 25% of all new websites, and there are more than 27 thousand plugins currently available. A pinch of tablet centric strategy can get your Word - Press site miles ahead of your competitors, so here are few strategies that will give your Wordpress websites and blogs an edge over your competitors:. s and intelligently including a substantial amount of key words in the title tags, image links, etc. This particular wordpress plugin is essential for not only having the capability where you improve your position, but to enhance your organic searches for your website. <br><br>These websites can be easily customized and can appear in the top rankings of the major search engines. If a newbie missed a certain part of the video then they could always rewind. This plugin is a must have for anyone who is serious about using Word - Press. You can up your site's rank with the search engines by simply taking a bit of time with your site. For a Wordpress website, you don't need a powerful web hosting account to host your site. <br><br>In case you have any concerns concerning where and also the best way to utilize [http://9ja.in/wordpress_dropbox_backup_648767 wordpress backup plugin], you can contact us with our own web page. This gives a clearer picture that online shoppers are familiar with the WP ecommerce system. s cutthroat competition prevailing in the online space won. If Gandhi was empowered with a blogging system, every event in his life would have been minutely documented so that it could be recounted to the future generations. The animation can be quite subtle these as snow falling gently or some twinkling start in the track record which are essentially not distracting but as an alternative gives some viewing enjoyment for the visitor of the internet site. If you have any questions on starting a Word - Press food blog or any blog for that matter, please post them below and I will try to answer them. <br><br>Google Maps Excellent navigation feature with Google Maps and latitude, for letting people who have access to your account Latitude know exactly where you are. And, that is all the opposition events with nationalistic agenda in favor of the individuals of Pakistan marching collectively in the battle in opposition to radicalism. Exacting subjects in reality must be accumulated in head ahead of planning on your high quality theme. The company gains commission from the customers' payment. Digital digital cameras now function gray-scale configurations which allow expert photographers to catch images only in black and white. <br><br>A sitemap is useful for enabling web spiders and also on rare occasions clients, too, to more easily and navigate your website. If you operate a website that's been built on HTML then you might have to witness traffic losses because such a site isn't competent enough in grabbing the attention of potential consumers. The days of spending a lot of time and money to have a website built are long gone. You should stay away from plugins that are full of flaws and bugs. You can check out the statistics of page of views for your web pages using free tools that are available on the internet.
	~~William O. Gustafson applied for a patent for the Impossiball design in 1981~~ and ~~it was issued in 1984.<ref>[http~~:~~//www.google.com/patents?id=koIzAAAAEBAJ&dq=US+4~~,~~474,376 Impossiball patent]</ref> [[Uwe Mèffert]] eventually bought the rights to some of the patents and continues to sell it in his puzzle shop under the Impossiball moniker~~.

	~~== Description ==~~
	~~The Impossiball~~ is ~~made in the shape~~ of ~~an [[icosahedron]] that has been rounded out to a sphere~~, and ~~has 20 pieces, all~~ of ~~them corners. The puzzle has twelve circles located at the vertices~~ of ~~the icosahedron~~, and ~~opposite circles are the same color~~. ~~Because~~ of the ~~rounded shape of the puzzle~~, ~~the pieces move up and down as they are rotated~~. It is ~~also possible~~ to ~~remove one piece, turning~~ the ~~puzzle into a spherical version~~ of the ~~[[15 puzzle]]~~.

	~~The purpose~~ of the ~~puzzle is to scramble the colors, and~~ then ~~restore it to its original state of having one color per circle~~. This ~~puzzle~~ is ~~equivalent to solving just the corners of~~ a ~~[[Megaminx]]~~. ~~The original Impossiball had the same colors as the Rubik~~'s ~~Cube: red, orange, yellow, green, blue and white. Meffert currently produces two versions, one~~ with ~~six colors and one with twelve. The six-color version (pictured) uses pink, two shades~~ of ~~orange, yellow, green and blue. All the pieces are still distinguishable, however, because the two pieces~~ with ~~the same three colors are mirror images of each other~~. ~~The twelve-color version has red~~, ~~pink, orange, yellow, two shades of green, three shades of blue, purple, brown and white~~.

	~~== Solutions ==~~
	In ~~spite of its daunting appearance~~ and ~~greater number of possible positions,~~ the ~~Impossiball is not much more difficult than the standard 2×2×2~~ [~~[Pocket Cube]~~]. This ~~is because it is not~~ a ~~deep-cut puzzle; it only has pentagonal face layers which~~ are ~~similar~~ in ~~structure to the square face layers of~~ the ~~cube~~. ~~There are no pieces~~ that ~~do not have a counterpart on~~ the ~~cube~~. ~~Many of the techniques employed~~ in the ~~solution of the Pocket Cube can also be adapted~~ for the ~~Impossiball.~~

	~~== Number~~ of ~~combinations ==~~
	~~There are 20!/2 ways to arrange~~ the ~~pieces~~, ~~since there is no way~~ to ~~create odd permutations without tampering with the puzzle~~. ~~There are 3~~<~~sup~~>19<~~/sup~~> ~~ways~~ to ~~orient the pieces~~, ~~since~~ the ~~orientation~~ of the ~~last depends on that~~ of the ~~preceding ones~~. ~~Since~~ the ~~Impossiball has no fixed face centers, this result is divided by 60~~. ~~There are 60 possible positions~~ and ~~orientations of the first corner, but all are equivalent because of the lack of face centers~~.

	:<~~math~~>~~\frac{20! \times 3^{19}}{120} \approx 2.36 \times 10^{25}~~<~~/math~~>
	~~The entire number~~ is ~~23 563 902 142 421 896 679 424 000 (roughly 23.6 septillion~~ on ~~the [[long~~ and ~~short scales\|short scale]] or 23~~.~~6 quadrillion on the long scale).~~

	~~== Records ==~~
	~~{{Empty section\|date=July 2008}}~~

	~~== See also ==~~
	*[[Rubik's ~~Cube]]~~
	*[[Megaminx]]
	*[[Dogic]]
	*[[Alexander'~~s Star]]~~
	*[[Combination puzzles]]

	~~==References==~~
	~~{{reflist}}~~

	~~== External links ==~~
	*[http://www.~~mefferts~~.~~com/ Meffert's puzzle shop]~~
	*[http://www.~~jaapsch.net/puzzles/impossi~~.~~htm Jaap's Impossiball page] — contains solutions and other information~~

	~~{{Rubik's Cube}}~~

	~~[[Category:Rubik's Cube permutations]]~~
	~~[[Category:Combination puzzles]]~~
	~~[[Category:Mechanical puzzles]]~~
	~~[[Category:Puzzles]]~~

en>Northamerica1000: - dated merge tag per Talk:Galois connection#Merge proposal

2012-09-25T09:13:11Z

- dated merge tag per Talk:Galois connection#Merge proposal

← Older revision		Revision as of 11:13, 25 September 2012
Line 1:		Line 1:
	~~First lets start by explaining the reasons why we need to put prime dressing on the backyard garden, high dressing is principally used to stage out an un-even lawn~~. ~~If you liked this short article and you would like to receive even more details regarding~~ [~~http~~:~~//lifepulp~~.~~com/profile/Joseph1604oqp1/ top dressing lawn with spreader~~] ~~kindly browse~~ through ~~our own site. With so many buffalo grass varieties accessible at this time~~, ~~and with so much questionable advertising surrounding this grass, receiving beneficial unbiased garden care recommendation has grow to be more important to Australians than ever before~~. ~~Prime dressing~~ is the ~~method~~ of ~~making use~~ of ~~compost~~, ~~soil, or sand over~~ the ~~surface of your garden~~. ~~Bacteria are by far~~ the ~~most abundant form of soil microbes~~ in ~~your soil~~.<br><br>~~Leaving it to dry before working it into to grass will help~~ the ~~dressing go all the way down~~ to ~~the base~~ of the ~~sward~~ and ~~also will assist~~ it ~~fill and aeration holes~~. The ~~back~~ of ~~a landscaper rake or a 5ft plank of wooden with a handle hooked up can be used~~ to ~~work the top dressing into the lawn. High dressing is an utility of~~ a ~~skinny layer of soil over a turf grass space~~ and ~~is used to easy and stage the surface or to change the soil situation~~, ~~often not more than ¼ to ½ inch~~.~~<br><br>In case you are scarifying the lawn in autumn (September is an efficient month for this) then you must do that BEFORE you top gown~~ the ~~garden. Otherwise the thatch (layer~~ of ~~lifeless grass) will probably be mixed in with~~ the ~~highest dressing~~ and ~~you will lose some high dressing and/or forestall~~ the ~~thatch from being effectively eliminated~~. ~~Improves~~ the ~~drainage on~~ the ~~lawn - High dressing may be applied following aeration (ideally hollowtining) to help create drainage channels through~~ the ~~basis zone~~. ~~Good soil resides soil.<br><br>If over-seeding keep in mind~~ to ~~maintain the soil moist~~, ~~but not moist, till~~ the ~~seeds have germinated. It reduces soil compaction and thatch by removing small plugs~~ of ~~small plugs of soil all through your yard~~. The ~~opposite time~~ to ~~do that is within~~ the ~~fall after~~ it ~~has began~~ to ~~chill down some~~. ~~I don't recommend doing this in the middle of summer season since grass can get confused due~~ to the ~~extreme heat and lack~~ of ~~rain~~.~~<br><br>Which merely means to dig out~~ the ~~affected lawn and put down clear sand in~~ the ~~indentation~~, and ~~then re-lay the lawn on high~~. ~~By eradicating the lawn in strips like roll on turf is completed~~, ~~the job becomes much easier~~ and ~~cleaner~~, and ~~could be done simply with a spade~~. ~~After reinstalling~~ the ~~turf strips~~, ~~lightly high dress~~ the ~~lawn to finish~~ the ~~evening out course~~ of ~~and the job will likely be completed~~.~~<br><br>Work out the scale~~ of ~~your lawn before you purchase; as a general guide a 2kg bag will be sufficient to high gown a sq. metre~~ of ~~garden~~. ~~Mow your lawn the day before making use~~ of ~~the highest dressing~~ and ~~rake up and remove any particles to allow~~ the ~~vitamins to successfully penetrate into~~ the ~~soil~~. ~~Hose the lawn totally in order that the dressing~~ is ~~barely seen. If the realm of lawn requiring night out~~ is ~~simply barely uneven then you possibly can apply~~ a ~~high dressing up~~ to ~~12mm directly. Mix topdressing soil mixture.<br><br>Any time within~~ the ~~energetic growing season is fine for high dressing indentations, from~~ the ~~start of Spring by way of to a month before Winter~~. ~~The old apply of prime dressing lawns with sand within the belief~~ that ~~it was~~ a ~~proper lawn care regime was fallacious~~. ~~The result~~ of ~~this continuing practice will only increase~~ the ~~garden higher and create layers~~ of sand and thatch that may solely ever have a detrimental impression on lawn health. The Lawn Guide is Australia's original impartial garden care advice site. Top gown.<br><br>E.g: If your lawn had a very high sand content it may endure from drought during dry periods, therefore by adding a peat based high dressing it might assist enhance the ~~drought resistance. Sand primarily based lawn - Any such lawn could~~ be ~~very free draining and liable to drought during scorching & dry climate~~. ~~Clay based mostly garden - Any such garden could be undergo from drainage issues throughout moist durations. A combination suitable for this garden would consist~~ of ~~two parts loam~~, ~~1 part peat & 4 components sand~~.<br><br>~~I'm additionally looking at making my very own topdressing as I have fairly a big space~~ to ~~cover~~, the ~~garden does not have much traffic...mainly myself and~~ the ~~mower~~. ~~Sort in~~ the ~~words Garden Renovation into the blog search facility and you will see a post that starts 'I'm often asked~~ by ~~friends~~.~~..'~~ and ~~this lists~~ the ~~order of play~~ of the ~~garden renovation process a bit like a move chart. High-dressing helps the garden in a lot~~ of ~~ways~~.<br><br>~~However, in case you are only top dressing lightly you possibly can add the garden seed first in order that the dressing goes on top thereby insulating the seed considerably from birds and rain~~. ~~Relying~~ on ~~which ebook you learn some even advise mixing~~ the ~~top dressing~~ and ~~seed to save lots of time~~. ~~Unfortunately it seems to make more work with the seed going where the top dressing goes - into the dips and none~~ on the ~~bumps! Mow the lawn on the brief side~~ and ~~apply dry dressing on a dry day to a dry garden.~~		[[Image:Impossiball solved.jpg\|thumb\|The Impossiball in its solved state.]]
			[[Image:Impossiball scrambled.jpg\|thumb\|The Impossiball in a scrambled state.]]
			[[Image:Impossiball turned.jpg\|thumb\|The Impossiball partway through a turn, showing how the pieces lift up.]]

			The '''Impossiball''' is a rounded [[icosahedron\|icosahedral]] puzzle similar to the [[Rubik's Cube]]. It has a total of 20 movable pieces to rearrange, same as the Rubik's Cube, but all of the Impossiball's pieces are corners, like the [[Pocket Cube]].

			== History ==
			William O. Gustafson applied for a patent for the Impossiball design in 1981 and it was issued in 1984.<ref>[http://www.google.com/patents?id=koIzAAAAEBAJ&dq=US+4,474,376 Impossiball patent]</ref> [[Uwe Mèffert]] eventually bought the rights to some of the patents and continues to sell it in his puzzle shop under the Impossiball moniker.

			== Description ==
			The Impossiball is made in the shape of an [[icosahedron]] that has been rounded out to a sphere, and has 20 pieces, all of them corners. The puzzle has twelve circles located at the vertices of the icosahedron, and opposite circles are the same color. Because of the rounded shape of the puzzle, the pieces move up and down as they are rotated. It is also possible to remove one piece, turning the puzzle into a spherical version of the [[15 puzzle]].

			The purpose of the puzzle is to scramble the colors, and then restore it to its original state of having one color per circle. This puzzle is equivalent to solving just the corners of a [[Megaminx]]. The original Impossiball had the same colors as the Rubik's Cube: red, orange, yellow, green, blue and white. Meffert currently produces two versions, one with six colors and one with twelve. The six-color version (pictured) uses pink, two shades of orange, yellow, green and blue. All the pieces are still distinguishable, however, because the two pieces with the same three colors are mirror images of each other. The twelve-color version has red, pink, orange, yellow, two shades of green, three shades of blue, purple, brown and white.

			== Solutions ==
			In spite of its daunting appearance and greater number of possible positions, the Impossiball is not much more difficult than the standard 2×2×2 [[Pocket Cube]]. This is because it is not a deep-cut puzzle; it only has pentagonal face layers which are similar in structure to the square face layers of the cube. There are no pieces that do not have a counterpart on the cube. Many of the techniques employed in the solution of the Pocket Cube can also be adapted for the Impossiball.

			== Number of combinations ==
			There are 20!/2 ways to arrange the pieces, since there is no way to create odd permutations without tampering with the puzzle. There are 3<sup>19</sup> ways to orient the pieces, since the orientation of the last depends on that of the preceding ones. Since the Impossiball has no fixed face centers, this result is divided by 60. There are 60 possible positions and orientations of the first corner, but all are equivalent because of the lack of face centers.

			:<math>\frac{20! \times 3^{19}}{120} \approx 2.36 \times 10^{25}</math>
			The entire number is 23 563 902 142 421 896 679 424 000 (roughly 23.6 septillion on the [[long and short scales\|short scale]] or 23.6 quadrillion on the long scale).

			== Records ==
			{{Empty section\|date=July 2008}}

			== See also ==
			*[[Rubik's Cube]]
			*[[Megaminx]]
			*[[Dogic]]
			*[[Alexander's Star]]
			*[[Combination puzzles]]

			==References==
			{{reflist}}

			== External links ==
			*[http://www.mefferts.com/ Meffert's puzzle shop]
			*[http://www.jaapsch.net/puzzles/impossi.htm Jaap's Impossiball page] — contains solutions and other information

			{{Rubik's Cube}}

			[[Category:Rubik's Cube permutations]]
			[[Category:Combination puzzles]]
			[[Category:Mechanical puzzles]]
			[[Category:Puzzles]]

en>JustAGal: Disambiguated: posets → Partially ordered sets

2012-05-30T15:24:32Z

Disambiguated: posets → Partially ordered sets

New page

First lets start by explaining the reasons why we need to put prime dressing on the backyard garden, high dressing is principally used to stage out an un-even lawn. If you liked this short article and you would like to receive even more details regarding [http://lifepulp.com/profile/Joseph1604oqp1/ top dressing lawn with spreader] kindly browse through our own site. With so many buffalo grass varieties accessible at this time, and with so much questionable advertising surrounding this grass, receiving beneficial unbiased garden care recommendation has grow to be more important to Australians than ever before. Prime dressing is the method of making use of compost, soil, or sand over the surface of your garden. Bacteria are by far the most abundant form of soil microbes in your soil. Leaving it to dry before working it into to grass will help the dressing go all the way down to the base of the sward and also will assist it fill and aeration holes. The back of a landscaper rake or a 5ft plank of wooden with a handle hooked up can be used to work the top dressing into the lawn. High dressing is an utility of a skinny layer of soil over a turf grass space and is used to easy and stage the surface or to change the soil situation, often not more than ¼ to ½ inch. In case you are scarifying the lawn in autumn (September is an efficient month for this) then you must do that BEFORE you top gown the garden. Otherwise the thatch (layer of lifeless grass) will probably be mixed in with the highest dressing and you will lose some high dressing and/or forestall the thatch from being effectively eliminated. Improves the drainage on the lawn - High dressing may be applied following aeration (ideally hollowtining) to help create drainage channels through the basis zone. Good soil resides soil. If over-seeding keep in mind to maintain the soil moist, but not moist, till the seeds have germinated. It reduces soil compaction and thatch by removing small plugs of small plugs of soil all through your yard. The opposite time to do that is within the fall after it has began to chill down some. I don't recommend doing this in the middle of summer season since grass can get confused due to the extreme heat and lack of rain. Which merely means to dig out the affected lawn and put down clear sand in the indentation, and then re-lay the lawn on high. By eradicating the lawn in strips like roll on turf is completed, the job becomes much easier and cleaner, and could be done simply with a spade. After reinstalling the turf strips, lightly high dress the lawn to finish the evening out course of and the job will likely be completed. Work out the scale of your lawn before you purchase; as a general guide a 2kg bag will be sufficient to high gown a sq. metre of garden. Mow your lawn the day before making use of the highest dressing and rake up and remove any particles to allow the vitamins to successfully penetrate into the soil. Hose the lawn totally in order that the dressing is barely seen. If the realm of lawn requiring night out is simply barely uneven then you possibly can apply a high dressing up to 12mm directly. Mix topdressing soil mixture. Any time within the energetic growing season is fine for high dressing indentations, from the start of Spring by way of to a month before Winter. The old apply of prime dressing lawns with sand within the belief that it was a proper lawn care regime was fallacious. The result of this continuing practice will only increase the garden higher and create layers of sand and thatch that may solely ever have a detrimental impression on lawn health. The Lawn Guide is Australia's original impartial garden care advice site. Top gown. E.g: If your lawn had a very high sand content it may endure from drought during dry periods, therefore by adding a peat based high dressing it might assist enhance the drought resistance. Sand primarily based lawn - Any such lawn could be very free draining and liable to drought during scorching & dry climate. Clay based mostly garden - Any such garden could be undergo from drainage issues throughout moist durations. A combination suitable for this garden would consist of two parts loam, 1 part peat & 4 components sand. I'm additionally looking at making my very own topdressing as I have fairly a big space to cover, the garden does not have much traffic...mainly myself and the mower. Sort in the words Garden Renovation into the blog search facility and you will see a post that starts 'I'm often asked by friends...' and this lists the order of play of the garden renovation process a bit like a move chart. High-dressing helps the garden in a lot of ways. However, in case you are only top dressing lightly you possibly can add the garden seed first in order that the dressing goes on top thereby insulating the seed considerably from birds and rain. Relying on which ebook you learn some even advise mixing the top dressing and seed to save lots of time. Unfortunately it seems to make more work with the seed going where the top dressing goes - into the dips and none on the bumps! Mow the lawn on the brief side and apply dry dressing on a dry day to a dry garden.